# Not micro. This post just gathers some economic equations that I need in future posts. The following equations are straight from macroeconomics 101. Nothing special at all. The one thing that is remarkable, though, is the number of times I had to explain these equations to people that had, unlike me, been to lectures on macroeconomics. Especially here in Germany these equations seem to be unknown. I have to explain them every single time I have a discussion about economic issues with a German.

The other reason for this post is to try Latex for the first time (not really needed here but we might need higher math, like divisions,  later). $S - I = Ex - Im$

The difference between savings $S$ and investments $I$ equals the difference between exports $Ex$ and imports $Im$. Simple, yet important.

Let us start with the gross domestic product $Y$. It is given as the sum $Y = C + I + G + NX$,

where

• $C$ is the consumption,
• $I$ is the investment,
• $G$ is government spending, and
• $NX$ is the difference between exports and imports.

Next we consider savings. National savings $S_{\mbox{\tiny national}}$ consist of two parts: private savings $S_{\mbox{\tiny private}}$ and government savings $S_{\mbox{\tiny government}}$: $S_{\mbox{\tiny national}} = S_{\mbox{\tiny private}} + S_{\mbox{\tiny government}}$

The private savings $S_{\mbox{\tiny private}}$ are equal to the private disposable income minus consumption. You can either spend money or you save it. Thus $S_{\mbox{\tiny private}} = \mbox{private disposable income} - \mbox{consumption}$,

or $S_{\mbox{\tiny private}} = (Y - T + TR +INT) -C$,

where

• $T$ are the taxes,
• $TR$ are transfer payments from the government, and
• $INT$ are interest payments on government debt.

The government, also, can only spend or save. Here we have: $S_{\mbox{\tiny government}} = \mbox{government income} - \mbox{government spending}$.

This gives $S_{\mbox{\tiny government}} = (T - TR - INT) - G.$

For the national savings we then get $S_{\mbox{\tiny national}} = S_{\mbox{\tiny private}} + S_{\mbox{\tiny government}} = Y - C - G$

Given what we know about the gross domestic product from above we obtain: $S_{\mbox{\tiny national}} = I + NX$

This is the equation that we wanted to obtain.